| Abstract: | By combining the ideas of Cartan's equivalence method and the method of the equivariant moving frame for pseudo-groups, we develop an efficient method for solving a wide variety of equivalence problems. The key is a pseudo-group analog of the classic result that characterizes congruence of submanifolds in Lie groups in terms of equivalence of the Lie group's Maurer-Cartan forms. This result, when combined with the fundamental recurrence formulas for the moving frame for pseudo-groups, will allow for a hybrid equivalence method that computationally improves on and illuminates both its progenitors. |
